Fritzsche Formula at Standard Conditions Equation and Calculator

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Fritzsche Formula at Standard Conditions Equation and Calculator

Fritzsche Formula for Pressure Change at Standard Conditions Equation and Calculator

The Fritzsche formula uses the friction factor f calculated from the following equation:

Equation 1
F = 0.02993 ( T_s / ( P_s Q_s ) ^1/7

where:

f = friction factor
T_s = temperature at standard conditions, °R
P_s = pressure at standard conditions, psia
Q_s = volume flow rate at standard conditions, SCFM

The Fritzsche formula for pressure drop then becomes

Equation 2
ΔP = ( 9.8265 x 10^-4 ) T L / ( P d⁵ ) ( P_s Q_s / T_s )^1.857

where:

ΔP = pressure drop, psi
L = pipe length, ft
d = pipe inside diameter, in
T = airflow temperature, °R
P = average air pressure, psia
Q_s = volume flow rate at standard conditions, SCFM
P_s = pressure at standard conditions, psia
T_s = temperature at standard conditions, ◦R

And in terms of flow rate and the upstream and downstream pressures, this becomes

Equation 3
Q_s = 29.167 T_s / P_s [ ( P₁² - P₂² ) d⁵ ) / ( T L )] ^0.538

where:

Q_s= volume flow rate at standard conditions, SCFM
P_s = pressure at standard conditions, psia
P₁= upstream pressure, psia
P₂= downstream pressure, psia
L = pipe length, ft
d = pipe inside diameter, in
T_s = temperature at standard conditions, °R
T = airflow temperature, °R

The preceding formulas can be used for the flow of air at standard conditions and any flowing temperatures. When standard conditions of 14.7 psia and 60°F are used along with a flowing temperature of 60°F, the preceding formulas can be simplified as follows:

Equation 4
ΔP = L Q_s^1.857 / ( 1480 P d⁵ )

where:

ΔP = pressure drop, psi
L = pipe length, ft
Qs = volume flow rate at standard conditions, SCFM (see equation 5)
d = pipe inside diameter, in
P = average air pressure, psia

Equation 5
Q_s = 1 / 35 [ ( P₁² - P₂² ) d⁵ ) / L ]^0.538

where:

Q_s = volume flow rate at standard conditions, SCFM
P₁ = upstream pressure, psia
P₂ = downstream pressure, psia
L = pipe length, ft
d = pipe inside diameter, in

Where air pressures are low and close to the atmospheric pressure such as in ventilating work and in airflow through ducts, we can modify the Fritzsche formula to calculate the pressure drops in in H₂O. Since 1 in of water column is equal to 0.03613 psi, the pressure loss can be expressed as follows:

Equation 6
h = L Q_s^1.857 / ( 785 d⁵ )

where h is the pressure drop measured in in H₂O.

Equation 7
Q_s = ( 785 h d⁵ / L )^0.538

Reference:

Piping Calculations Manual,
E. Shashi Menon
SYSTEK Technologies, Inc